5 papers
The relative isoperimetric profile of a unit square with a central square removed
Kyle Byassee, Hunter Johnson, Brandon Jones +1
We calculate the exact values of the relative isoperimetric profile for a unit square with a central square removed. In other words, given a removed central square of a fixed size,…
Remarks on the relative isoperimetric profile of polygonal domains in
Jason DeVito, Robert DeYeso, Ezra Nance +1
We develop techniques for solving the relative isoperimetric problem on polygonal domains in , with special attention paid to corners. As an application, we solve the…
Almost Bijective Parametrization of Copositive Univariate Polynomials
Hoon Hong, Ezra Nance
In this work we develop a novel recursive method for parametrizing the cone of copositive univariate polynomials of any arbitrary degree . This parametrization is surjective, al…
Almost Bijective Parametrization of Copositive Matrices
Hoon Hong, Ezra Nance
In this work we take a deep dive into the cone of copositive matrices. In doing so we visualize the cone, make geometric observations about it, and prove them. We then…
Almost positive curvature on an irreducible compact rank 2 symmetric space
Jason DeVito, Ezra Nance
A Riemannian manifold is said to be almost positively curved if the sets of points for which all -planes have positive sectional curvature is open and dense. We show that the Gr…